diff --git a/R/units.R b/R/units.R
index d87ece6..70aaa25 100644
--- a/R/units.R
+++ b/R/units.R
@@ -17,7 +17,7 @@
 #' u(100, "m") > u(1, "km")
 #'
 #' @export
-u <- function(x, unit) {
+u <- function(x, unit = "1") {
   stopifnot(is.numeric(x))
   stopifnot(is.character(unit))
   # x must be a pure number
@@ -46,9 +46,12 @@ u <- function(x, unit) {
 #'  # from x in units of "meter"
 #'  du(x, "m")
 #'
+#'  # drop the unit of a dimensionaless "unit" quantity
+#'  du(x / x)
+#'
 #' @seealso [units::drop_units()]
 #' @export
-du <- function(x, unit) {
+du <- function(x, unit = "1") {
   stopifnot(inherits(x, "units"))
 
   if (has_comp_unit(x, unit)) {
diff --git a/man/du.Rd b/man/du.Rd
index 9adf445..4244677 100644
--- a/man/du.Rd
+++ b/man/du.Rd
@@ -4,7 +4,7 @@
 \alias{du}
 \title{Drop physical units from a quantity}
 \usage{
-du(x, unit)
+du(x, unit = "1")
 }
 \arguments{
 \item{x}{A dimensionful numeric vector (S3 class "units"), e.g. generated with \code{\link[=u]{u()}} or
@@ -27,6 +27,9 @@ The dimensionless number is defined by the ratio of \code{x} and one unit \code{
  # from x in units of "meter"
  du(x, "m")
 
+ # drop the unit of a dimensionaless "unit" quantity
+ du(x / x)
+
 }
 \seealso{
 \code{\link[units:drop_units]{units::drop_units()}}
diff --git a/man/u.Rd b/man/u.Rd
index b986c4b..b8a65ec 100644
--- a/man/u.Rd
+++ b/man/u.Rd
@@ -4,7 +4,7 @@
 \alias{u}
 \title{Augment a quantity with a physical unit}
 \usage{
-u(x, unit)
+u(x, unit = "1")
 }
 \arguments{
 \item{x}{A numeric vector to be augmented with a unit.}
diff --git a/tests/testthat/test-units.R b/tests/testthat/test-units.R
index 28893c6..d997f03 100644
--- a/tests/testthat/test-units.R
+++ b/tests/testthat/test-units.R
@@ -21,4 +21,6 @@ test_that("du() works", {
 
   expect_equal(du(x, "m"), 1000)
   expect_error(du(x, "Hz"))
+
+  expect_equal(du(x/x), 1)
 })